Specification and Analysis of Concurrent Systems: The Cosy Approach

ISBN-13: 9783642773396 / Angielski / Miękka / 2011 / 480 str.

Ryszard Janicki; Peter E. Lauer

Opis

Concurrent systems abound in human experience but their fully adequate conceptualization as yet eludes our most able thinkers. The COSY (ConcurrentSystem) notation and theory was developed in the last decade as one of a number of mathematical approaches for conceptualizing and analyzing concurrent and reactive systems. The COSY approach extends theconventional notions of grammar and automaton from formal language and automata theory to collections of "synchronized" grammars and automata, permitting system specification and analysis of "true" concurrency without reduction to non-determinism. COSY theory is developed to a great level of detail and constitutes the first uniform and self-contained presentationof all results about COSY published in the past, as well as including many new results. COSY theory is used to analyze a sufficient number of typical problems involving concurrency, synchronization and scheduling, to allow the reader to apply the techniques presented tosimilar problems. The COSY model is also related to many alternative models of concurrency, particularly Petri Nets, Communicating Sequential Processes and the Calculus of Communicating Systems.

Spis treści

1 What COSY Is and What It Is For.- 1.1 Introduction.- 1.2 Concepts, Objectives and Design Decisions.- 1.3 Structure of Bookevevr.- 1.4 Acknowledgements.- 2 Formal Theory of Basic COSY.- 2.1 Basic COSY Syntax and Semantics.- 2.2 VFS Semantics of COSY.- 2.2.1 Simple Properties of Vector Sequences.- 2.2.2 Vector Sequences and Partial Orders.- 2.2.3 Vector Sequences of Path Programs.- 2.2.4 Concurrent Product of Regular Expressions.- 2.3. Petri Net Semantics of COSY.- 2.3.1 Elements of Net Theory.- 2.3.2 VFS semantics of SMD nets.- 2.3.3 Semantics of Labelled Petri Nets.- 2.3.4 Labelled Petri Nets defined by Path Programs.- 2.3.5 Uniquely Named and Labelled Uniquely Named Regular Expressions.- 2.3.6 Labelled Nets and Products of Regular Expressions.- 2.3.7 Labelled Nets and COSY Path Programs.- 2.3.8 Other Constructions.- 2.4 Adequacy Properties of Path Programs.- 2.4.1 Syntactically Conflict-Free Path Programs.- 2.4.2 Checking Adequacy of SCF-Path Programs.- 2.4.3 Adequacy-Preserving Transformations.- Insertions Preserving Adequacy.- Deletions Preserving Adequacy.- Applications of Adequacy-Preserving Transformations.- 2.4.4 Free-Choice Path Programs.- 2.5 Execution Semantics for COSY.- 2.5.1 Execution Strategies.- 2.5.2 Maximally Concurrent Strategies.- 2.6 Semantics of COSY with Priorities.- 2.6.1 Observations and Multiple Sequences.- 2.6.2 MFS Semantics for Priority COSY.- 2.6.3 Starvation Problem.- 2.6.4 Infinite MFS and Formal Definition of Starvation.- 2.6.5 Simulation of Dynamic Priorities.- 2.6.6 VFS Semantics for Priority COSY.- 2.7 Bibliographic Notes.- 3 High-level COSY Programs and System Design.- 3.1 High-level COSY Syntax and Semantics.- 3.2 The Process Notation.- 3.3 Macro Generators for COSY Notation.- 3.3.1 The Macro Program.- 3.3.2 The Collectivisors.- 3.3.3 The Body-Replicators.- 3.3.4 Macro Paths and Macro Processes.- 3.3.5 Sequence Replicators.- 3.3.6 Left and Right Sequence Replicators.- 3.3.7 The Distributors.- 3.3.8 Expansion of Macro COSY Programs.- The Expansion of Replicators.- The Expansion of Distributors.- Expansion Theorem.- 3.4 The Semantics of Macro COSY Programs.- 3.5 The COSY Environment.- 3.5.1 The Architecture of BCS.- The BCS Analysis Mechanism.- The BCS Semantic Transformation Mechanism.- The BCS Interface.- 3.5.2 The Macro COSY Environment.- 3.6 The COSY System Dossier.- 3.7 Bibliographical Notes.- 4 COSY Applications.- 4.1 Two-Way Channel with Disconnect.- 4.1.1 Bibliographic Notes.- 4.2 The Hyperfast Banker.- 4.2.1 The Bank Director.- 4.2.2 The Vault.- 4.2.3 The Doors.- 4.2.4 The Fair Doormen.- 4.2.5 The Counters.- 4.2.6 The Clerks.- 4.2.7 The Fair Reimbursers.- 4.2.8 The Customers.- 4.2.9 Priority Constraints.- 4.2.10 Final Comment and Bibliographical Notes.- 4.3 Cigarette Smokers.- Bibliographic Notes.- 4.4 Merlin-Randell Problem of Train Journeys.- 4.4.1 Movement Graphs and Minimal Critical Patterns.- 4.4.2 COSY Specification of the Synchronization.- 4.4.3 Final Comment and Bibliographic Notes.- 4.5 Transforming Sequential Systems into Concurrent Systems.- 4.5.1 e-Paths and e-Path Programs.- 4.5.2 Concurrent e-Paths and Proper Concurrent e-Paths.- 4.5.3 Synchronized e-Path Programs.- 4.5.4 Final Comment and Bibliographic Notes.- 4.6 Modelling N-Modular Redundancy.- 4.6.1 Replicated Computation in Networks of Computing Nodes.- 4.6.2 Formal Specification.- 4.6.3 Bibliographical Notes.- 5 Comparison of COSY with Other Models.- 5.1 COSY and CCS.- 5.2 COSY and CSP.- Full COSY and Petri Nets.- 5.3.1 Uniquely Named Comma&Star-free Programs and Asymmetric Choice Nets.- 5.3.2 Priority Path Programs, Priority Nets and Inhibitor Net.- 5.4 Vector Sequences and Mazurkiewicz Traces.- 5.5 COSY and Synchronized Behaviours.- 6 Historical Perspective.- 6.1 Introduction.- 6.2 Conceptual and Methodological Framework of COSY Approach.- Appendices.- A Algebra of Relations.- B Automata and Formal Language Theory.- B.1 Strings.- B.2 Languages.- B.3 Regular Expressions and Languages.- B.4 Finite State Automata and Grammars.- C Elements of Graph Theory.- D Proofs of Theorems 2.25, 2.26 and 2.28.- E Proofs of Theorems 2.37 and 2.38.- F Proof of Theorem 2.29.- G Proof of Theorem 4.3.- H Basic COSY Notations and Macro COSY Notation.- List of Figures.- List of Algorithms.- List of Definitions.- List of Theorems.- List of Corollaries.- List of Lemmas.

O autorze

The COSY formalism facilitates the abstraction of synchronizational aspects of concurrent and reactive systems, and their analysis. The COSY theory is developed in detail and proofs of major results are given in full. Applications of COSY to practical problems are given.